does caliper sticking will damage the rotor?

 

only if its hitting the rotor, which it shouldnt be... only thing that will happen is the pads will wear unevenly... one will wear more than the other.

Get the slider bolts off, grease them up well with a high-temp grease... clean out the old grease from the holes and re-install them... that should free them up.

 

But THAT will cause overheating. If its bad enough, it can warp your rotor, or damage the seals in the caliper. Either way, you'll notice it.